2.3. Penalized Cox Regression

Concept

Feature selection is an useful strategy to avoid over-fitting, to obtain more reliable predictive results, and to provide more insights into the underlying casual relationships (Ma and Huang, 2008). In this section, a feature selection can be performed using ridge, elastic net or lasso penalty, especially when there are too many predictors (e.g. n<<p). More information can be found in Zou and Hastie, 2005, Freidman et al, 2008 and Simon et al, 2011.

Usage

A Penalized Cox regression analysis can be conducted by applying the following steps:

1. Select the analysis method as Penalized Cox Regression from Analysis tab.
2. Select suitable variables for the analysis, such as survival time, status variable
3. If all predictors are continious then one can check the Select All Variables option to include all variables in dataset to the feature selection process. If some predictors categorical and others are continious, then uncheck the Select All Variables option and select categorical and continuous variables seperately.
4. Define the penalty term using the Penalty term slider as follow:

Penalty term = 0: ridge penalty 0 < Penalty term < 1: elastic net penalty Penalty term = 1: lasso penalty

5. Select the number of folds for cross-validation. Note that number of folds must be greater than 3.
6. Click Run button to run the analysis.

Outputs

a) Variables in the model

Variable selection is conducted with the selected penalized method (i.e. ridge, elasticnet, lasso) and results will be displayed as a table, which includes selected variables and their associated coefficient estimates.

b) Cross-validation curve

A cross-validation curve can be created to investigate the relationship between partial likelihood devaince and lambda values.